The Axiomatic Trader: Latent Regularity, Information Budgets, and the Canonical Form of a Quantitative Investment System

Abstract

Systematic trading rests on one article of faith: that regularities found in the past persist. This paper does three things. First, it states that faith as five axioms, each a commonplace practitioners already accept: (A1) a decision may use only what was known when it was made; (A2) what looks like the market changing its rules is the market changing its unobserved state, the machinery being the same in every era; (A3) the future may replay stretches of the past, though not in history's proportions; (A4) states persist for a while, and the dependence they carry eventually dies out; (A5) whatever predictability exists is slight, even for a rule that knows the state. What turns these into axioms is quantification, and the quantities are declared rather than estimated: an invariance defect $\varepsilon_0$, a recurrence bound $\Lambda$ at a block scale $b$, coherence times $\ell_i$, a signal ceiling $\rho$ and an invariance ratio $\kappa$. These five declarations are the whole of the premises'empirical content. Second, it proves that the axioms force a five-stage canonical form for a quantitative investment system -- a declared representation, a capacity-bounded shrunk ensemble, contiguous purged block evaluation aggregated by $\mathrm{CVaR}_{1/\Lambda}$, a budgeted and deflated search, robust fractional Kelly sizing -- each stage necessary: a procedure omitting it does strictly worse under a law the axioms admit. Third, it tests the axioms where they are falsifiable, each only at its declared constants, on real market series: no axiom is so far overturned; what the data reject are particular declarations, the conservative $\kappa = 1$ and the exponential decay instance among them.